Surface dynamics of Bi2CaSr2Cu2O8

Physica B 219&220 (1996) 431-433

ELSEVIER

Surface dynamics of Bi2CaSr2Cu208 F.W. de Wette a'*, U. Paltzer a'b, U. Schr6der b aDepartment of Physics, University of Texas, Austin, TX 78712. USA blnstitute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany

Abstract

We interpret the inelastic He-scattering results for the Bi-O(00 1) surface of Bi2CaSr2Cu208, which exhibits an anisotropic superstructure. With a shell model calculation, which takes account of the superstructure, we account for the measurements and show that the appearance of rather dispersionless surface modes and the great similarity between the surface mode spectra in the (1 1 0) and (1 0 0 ) directions are direct results of the anisotropic superstructure. These features are some of the first examples of unexpected manifestations of a superstructure of a surface in the dynamics of that surface.

The structural and dynamical properties of the BiO(00 1) surface of Bi2CaSrzCu208 (Bi-2122) were measured a few years ago with helium atom diffraction and inelastic scattering [1, 2]. The diffraction revealed a fivefold superstructure on the surface ((1 i 0) -direction), of the kind earlier found for the bulk [3, 4]. The inelastic time of flight (TOF) measurements were made in the (1 1 0) and (1 0 0 ) directions. In Fig. la we show the primitive two-dimensional (2D) surface unit cell (al, a2), the non-primitive x/2 x x/2(R45 °) cell (A1, A2), and the five-fold superstructure cell (A1, 5A:z). Fig. l b shows the surface Brillouin zone (SBZ) of the cell (Ax, A2), corresponding to the reciprocal lattice vectors B1, B2, and the SBZ of the five-fold superstructure, corresponding to B1, ½ B2 (heavy outline; four equivalent extended zones are also indicated). Fig. l(c) shows the SBZ (heavy outline) for a commensurate 19-fold superstructure, as well as 18 extended zones. The results of the T O F measurement for 2D wave vectors along the directions (1 10) (F--M/2) and ( 1 0 0 ) ( F - J ? ) are shown in Fig. 2. In addition to measurements of the familiar acoustic Rayleigh mode *Corresponding author.

(R), there appear to exist optical modes (02, 03, 04) with little or no dispersion (cf. Refs. [1, 2]). We also notice that the modes measured along F - )? (indicated by x ) are very similar to those measured along r - 1~/2 (indicated by IS]). We will show that this is a direct consequence of the superstructure. To interpret these data we performed the first realistic calculation of the surface phonons of a high-Tc superconducting compound (HTSC). We followed our general approach for calculating bulk phonons and phonon-related properties of HTSC (cf. Ref. [5]). Since equilibrium considerations are of prime importance for the relaxation of the surface, the bulk shell model was made to satisfy the static equilibrium conditions for the bulk crystal. The model was then used to evaluate the surface relaxation of a slab of Bi-2122 material bounded by Bi-O(0 0 1) surfaces. The lattice dynamical calculations for the slab yield all the phonon energies together with their polarization vectors. The phonons for which the main vibration takes place in the surface planes are the surface phonons. It turns out that a full dynamical calculation for a slab, including the five-fold or 19-fold superstructure, exceeds our computational resources. However, we can get around this difficulty as follows: because of the

0921-4526/96/$15.00 (~, 1996 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 7 6 8 - 7

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F. W. de Wette et al. /Physica B 219&220 (1996) 431-433

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10 superstructure, there exists equivalence between the results of a true superstructure calculation (unit cell A1, 5A1) for wave vectors along F - 4 / 2 , on the one hand, and the sum of the results of calculations performed for the isotropic 2D-cell (At, A2) for wave vectors along F -- )~f/2, as well as for wave vectors pointing from F to the central lines of the extended zones (in Fig. lb,c), on the other (for details see Paltzer et al. [6]). The results of this procedure are shown in Fig. 3. In the left panel are plotted the dispersion curves of vibrations perpendicular to the surface (SP±), of the Bi particle at the surface.These curves represent the Rayleigh mode of the superstructure. The right panel is a similar plot of the SPII mode of the surface in which the surface particles vibrate mainly in the surface plane, in the direction of the wave vector. We see that these SP± and SPII dispersion curves jointly cover the entire area in the wave vector-phonon energy plane of Fig. 2 where the experimental points are located. A more detailed understanding of the measurements is obtained from scan curve diagrams of the helium scattering, in an extended zone representation of the experimental points. A scan curve represents the wave vector-energy relation of the helium atoms, for which the kinematical conditions of energy- and crystal m o m e n t u m conservation are fulfilled (for details cf. Ref. [7]). In Fig. 4 are plotted the scan curves of the measurements

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(dotted lines), for incident wave vector ki = 5.8 ~ - 1 and incident angles 0i between 38 ° and 44 °. The experimental points are indicated by W; their replicas in the extended zones by 15].The intersections of the scan curves with the dispersion curves of Fig. 3 indicate possible

F. If. de Wette et al./Physica B 219&220 (1996) 431 433

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gap between 03 and 04 is reproduced; (4) 04 is predicted only partially. The successes of points 1 3 are extremely gratifying considering the fact that we had to take account of the superstructure in a purely geometrical way, since the interactions which give rise to the superstructure and the shifts in the particle positions are unknown. Finally, the similarity of the modes along the (1 1 0) and (1 0 0 ) directions is a direct consequence of the equivalence of the modes along r - 4 / 2 , and those along the central lines of the extended zones. Since the r - X- direction intersects these central lines, for wave vectors at these intersections the modes must be the same as for the corresponding wave vector (factor l / x / 2 shorter) along [" - 4 / 2 .

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Fig. 4. Scan curves (ki = 5.8 A- ~, Oi between 44'~and 48°), in an extended zone scheme. Measured phonon energies are indicated by ram;[] are replicas of these points in the extended zones. Peaks of the differential reflection coefficients are indicated by + . Upper left-hand corner: differential reflection coefficient along the 0~ = 40.5 scan curve. measurements. However, actual measurements depend in addition on the relevant helium differential reflection coefficients. In Fig. 4 we have indicated by + the locations of the peaks ( >/50 in arb. units) of the differential reflection coefficients, calculated along the scan curves. We note the following: (1) the acoustic branches below 5 meV show the right dispersion and a n u m b e r of points are reproduced correctly; (2) at higher energies the dispersion becomes flatter; 02 is reproduced nicely; (3) the

The authors acknowledge support by the Robert A. Welch Foundation, the Deutsche Akademische Austauschdienst, F O R S U P R A , and by a N A T O travel grant.

References [1] J.G. Skofronick and J.P. Toennies, in: Surface Properties of Layered Structures, ed. G. Benedek (Kluwer, Dordrecht, 1992) p. 151. [2] D. Schmicker, Doctoral Dissertation, G6ttingen (1993), unpublished. t-3] S.L. Tang et al., Physica C 56 (1988) 177. [4] R. Claessen et al., Phys. Rev. B 39 (1989) 7316. 1-5] F.W. de Wette, Comments Cond. Mat. Phys. 15 (1991) 225. 1-6] U. Paltzer et al., to be published. [7] J.P. Toennies, in: Surface Phonons, eds. W. Kress and F.W. de Wette (Springer, Berlin, 1991) p. l 11.